We use high signal-to-noise ratio long-slit spectra in the λλ3600–4700 range of the 20 brightest northern Seyfert 2 galaxies to study the variation of the stellar population properties as a function of distance from the nucleus. In order to characterize the stellar population and other continuum sources (e.g. featureless continuum, FC) we have measured the equivalent width,W, of six absorption features, four continuum colours and their radial variations, and performed spectral population synthesis as a function of distance from the nucleus. About half of the sample has Ca II K and G bandW values smaller at the nucleus than at 1 kpc from it, owing to a younger population and/or FC. The stellar population synthesis shows that, while at the nucleus, 75 per cent of the galaxies present contribution >20 per cent of ages 100 < - Myr and/or of an FC, this proportion decreases to 45 per cent at 3 kpc. In particular, 55 per cent of the galaxies have a contribution >10 per cent of the 3-Myr/FC component (a degenerate component in which one cannot separate what is caused by an FC or by a 3-Myr stellar population) at the nucleus, but only 25 per cent of them have this contribution at 3 kpc. As a reference, the stellar population of 10 non-Seyfert galaxies, spanning the Hubble types of the Seyfert (from S0 to Sc) was also studied. A comparison between the stellar population of the Seyferts and that of the non-Seyferts shows systematic differences: the contribution of ages younger than 1 Gyr is in most cases larger in the Seyfert galaxies than in non-Seyferts, not only at the nucleus but up to 1 kpc from it.